Excerpted from Wikipedia:

Krazy Kat is a comic strip created by George Herriman that appeared in U.S. newspapers between 1913 and 1944. It was first published in William Randolph Hearst's New York Evening Journal. Set in a dreamlike portrayal of Herriman's vacation home of Coconino County, Arizona, Krazy Kat's mixture of surrealism, innocent playfulness, and poetic language have made it a favorite of comics aficionados and art critics for more than eighty years.

The strip focuses on the relationship triangle between its title character, a carefree and innocent cat of indeterminate gender (referred to as both male and female), her antagonist Ignatz Mouse, and the protective police dog, Officer Bull Pupp. Krazy nurses an unrequited love for the mouse, but Ignatz despises her and constantly schemes to throw a brick at her head; for unknown reasons, Krazy takes this as a sign of affection. Officer Pupp, as Coconino County's administrator of law and order, makes it his unwavering mission to interfere with Ignatz's brick-tossing plans and lock the mouse in the county jail.

Despite the slapstick simplicity of the general premise, it was the detailed characterization, combined with Herriman's visual and verbal creativity, that made Krazy Kat one of the first comics to be widely praised by intellectuals and treated as serious art.  Gilbert Seldes, a noted art critic of the time, wrote a lengthy panegyric to the strip in 1924, calling it "the most amusing and fantastic and satisfactory work of art produced in America today." Famed poet E. E. Cummings, as another Herriman admirer, wrote the introduction to the first collection of the strip in book form. In more recent years, many modern cartoonists have cited Krazy Kat as a major influence.

Public reaction at the time was mixed; many were puzzled by its iconoclastic refusal to conform to comic strip conventions and simple gags. But publishing magnate William Randolph Hearst loved Krazy Kat, and it continued to appear in his papers throughout its run, sometimes only by his direct order.

All of the Sunday strips from 1916 to 1924 were reprinted by Eclipse Comics in cooperation with Turtle Island Press. The intent was to eventually reprint every Sunday Krazy Kat, but this planned series was aborted when Eclipse ceased business in 1992. Beginning in 2002, Fantagraphics has resumed reprinting Sunday Krazy Kats where Eclipse left off. Fantagraphics has released seven installments to date, designed by Chris Ware.

Krazy and Ignatz: The Komplete Kat Komics Vol. 1, 1916 hardcover at eBay